A Khintchine Decomposition for Free Probability

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Let μ be a probability measure on the real line. In this paper we prove that there exists a decomposition μ= μ₀ μ₁.. μₙ.. such that μ₀ is infinitely divisible and μᵢ is indecomposable for i ≥ 1. Additionally, we prove that the family of all -divisors of a measure μ is compact up to translation. Analogous results are also proven in the case of multiplicative convolution.